Magnetic suspension and propulsion system

ABSTRACT

A method and apparatus for supporting and translating a mass by magnetic attractive means. A ferromagnetic track may have repetitive magnetic discontinuities. A linear plural-phase ferromagnetic electric motor, which may be synchronous, supports the mass at a small gap below the track at zero frequency current variation through the motor. The same motor translates the mass along the track at a speed determined by the frequency of the plural-phase alternating current supplied to the motor. A nonlinear feedback circuit having plural sensor elements controls the magnitude of the alternating current supplied to the motor. This maintains the gap substantially constant despite varying loads and gradually corrects for unevenness of the track. The feedback circuit provides uniform stability and uniform dynamic response regardless of the length of the gap.

Ol-25-7Z XR 396389093 United States Patent 1151 3,638,093

Ross 1451 Jan. 25, 1972 1541 MAGNETIC SUSPENSION AND FOREIGN PATENTS RAPPLICATIONS PROPULSION SYSTEM 644,302 4/1937 Germany 707,032 6/1941Germany [72] Inventor. James A. Ross, La Jolla, Callf. 1,537,842 H1968France [73] Assignee: Rohr Corporation, Chula Vista, Calif. 1,165,704 I969 Great Britain 1,228,004 4/1971 Great Britain [22] 1971 643,3164/1937 Germany ..104/148 MS [21] Appl. No.: 131,041

Primary Examiner-D. F. Duggan Attorney-Harry R. Lubcke [52] U.S.C1..318/687,318/135,310/12, 308/10, 104/148 51 Int. 01. ..H02k 41/04 [57]ABSTRACT [58] Field of Search ..310/12-14, 162-164; A method andapparatus for supporting and translating a mass 318/687, 135, 121;104/148, 148 LM, 148 NS, 89; by magnetic attractive means. Aferromagnetic track may 308/10 have repetitive magnetic discontinuities.A linear plural-phase ferromagnetic electric motor, which may besynchronous, [56] Referen e Cit d supports the mass at a small gap belowthe track at zero frequency current variation through the motor. Thesame UNITED STATES PATENTS motor translates the mass along the track ata speed determined by the frequency of the plural-phase alternatingcurrent supplied to the motor. A nonlinear feedback circuit having833635 W906 Royers Q I I "308/10 X plural sensor elements controls themagnitudeof the alternatl o942 3/1912 Bachelet "310/14 ing currentsupplied to the motor. This maintams the gap sub- ]:020:943 3/1912Bachelet I I I t l "310/13 stantially constant despite varying loads andgradually cor- 310/13 rects for unevenness of the track. The feedbackcircuit pro- 04/89 vides uniform stability and uniform dynamic responsere- X gardless of the length of the gap.

2,870,349 1/1959 Rosenberg et al.. 3,125,964 3/1964 Silverman 3,158,76511/1964 Polgreen...

3,243,238 3/1966 Lyman ..308/10 34 Claims 10 Drawing Figures 3,407,74910/1968 Frig ..318/135 X 3,456,136 7/1969 Pierro ..310/12 3,470,82810/1969 Powell, Jr. et al ..310/13 X CCELEROMETER NETWORK 20 21 L ACOMPENSATING Y MULTIPLIER x (D.C.PATH) 24 sauna: ROOT CIRCUIT Z2 25 T 26Posmou COMPENSATING PERFEC RANSDUCER T DIFFERENTIATOR T WORK (kc. PATH)VEHICLE A IMPERFECT 1 A U T FLI R mrrenr-zn-mron l E LF QIBOLLABLE 2 I r1/ RAIL so THREE- 33 as MOTOR E SPEED PHASE B x 1 VARIABLE IMPERFECT n ar cournou. FREQ D'FFERENTIATOR FF uumpuen :r'Of ER U OSCILLATOR 1/ 34 I37 c mPERFEc'r c mrrsaznrmon J- 2 39 I: 0 POWER I PATENTEU JAR 2 5 572MEHBFG FIG'I l I I l l ll lllllllllll .l

l l l l l ll l'lllllll- FIGZ PATENTED JANZS I972 SHEET '& 0F 5 QwBOQ SnPATENTED JANZS I972 VOLTAGE CURRENT SUSPENSION HEIGHT LIFT VELOCITYMAGNETIC FLUX slsaslosa' SHEET 511? 6 /VOLTAGE VEHICLE LIFT VELOCITY TODESIRED GAP SUSPENSION OR HEIGHT OF VEHICLE ABOVE GROUND RAIL r" r 5 H7KMAGNETIC FLUX CURRENT VOLTAGE IO I I T4 N6 II 35' SUSPENSION CONTROLFIG. 5

VOLTAGE FREQUENCY MAGNETIC FLUX VEHICLE VELOCITY F IG. 6

1 MAGNETIC SUSPENSION AND PROPULSION SYSTEM BACKGROUND OF THE INVENTIONThis-invention pertains to a method and means for accomplish-ingcontrolled support and motion of a mass by electrically producedmagnetic means.

Prior systems have provided magnetic support for a wide range ofdevices, from gyroscope and ultracentrifuge bearings to railway carsupon a track. For railway cars magnetic repulsion has frequently beenemployed, with a stationary structure below, a supported structureabove, and a magnetic flux gap between.

In order to .obtain a constant force with displacement characteristicsuitable for known linear feedback circuits, a second magnetic meanshasoften been positioned below the supported structure. Feedback isrequired to keep the supported structure properly related to thestationary structure below it. Such two-gap structures are applicable torotational magnetic devices, such as gyroscopes and ultracentrifuges.

Prior single-gap structures have used linear feedback and have hadrestricted ranges of gap variation over which the system can be stable.Again, these are applicable to ultracentrifuges or accelerometers, whichdo not require large ratios of gap variation.

Magnetic propulsion has been proposed and employed having a pair offerromagnetically related windings astride a stationary rail conductorin which eddy currents are produced. Such a propulsion system typicallyemploys aircushion support and guidance for the vehicle and in somecases an air bearing for close control of the air gaps between the motorand the reaction rail.

Other propulsion systems have required a large plurality of stationarycoils in the roadway, with superconducting electromagnets in the vehiclewhich traverses it, or a large plurality of permanent magnets in boththe roadway and the vehicle. This accomplishes suspension, but othermeans are required for propulsion. Even further arrangements haveproposed electromagnetic support but employ air propulsion; as with apropeller or jet element upon the vehicle, or pneumatic means to forcethe vehicle through an airtight tube.

For vehicular transportation the degree of stability of the vehicle withrespect to the track is important, as in the compensation for varyingweight upon discharging passengers, varying thrust due to wind, and thesmoothness of the ride. The latter depends upon the dynamic response ofthe system over the whole range of airgap. The showings of the prior artin these important respects have been highly fragmentary or nonexistent.

SUMMARY OF THE INVENTION A mass is supported and advantageously alsopropelled by a single attractive magnetic field. This may be a vehiclearranged to run along a two spaced rail way and employing four (or more)wound linear motors, which are a part of the mass. Two of the motors arecoactive with each rail by suspension below the same. Alternately, amonorail way with two or more aligned motors may be used.

Therail is ferromagnetic. Typically, it has repetitive magneticdiscontinuities to allow propulsion by variable reluctance.

A linear motor has a ferromagnetic core, with plural-phase windings inslots. The motor extends over plural magnetic discontinuities in therail.

A nonlinear feedback circuit includes a first sensor element sensing thelength of the gap between the motor and the rail and a second sensorelement sensing the acceleration with which changes in this length mayoccur. Also included is an integrator that is connected to the gapsensor. The output of the integrator, along with the electrical responseof the acceleration sensor element, are processed through asquare-rooter electrical element, and thenthrough an electricaldifferentiator. In parallel with the electrical differentiator, amultiplier forms the product of the instantaneous displacement and thesquare-rooter output. This output controls the current in theplural-phase windings of the motor.

This feedback circuit provides feedback gain that is substantiallyconstant with respect to the length of the gap. Moreover, this constancyof gain is substantially unaffected by changes in the frequency of theplural-phase alternating current which drives the vehicle at a speedproportional to that frequency.

The feedback circuit maintains the gap substantially constant despitevarying loads and gradually corrects for unevenness of the track.lmportantly, the stability of the vehicle upon the track and the dynamicresponse of the control is uniform regardless of the length of theairgap. The feedback circuit also maintains lateral stability and anylateral perturbation is restored in a damped manner without overshoot.

The essentials of the system; the rails and particularly the linearmotors, are relatively lightweight and inexpensive. A saving in weightby a factor of two or better is achieved in the vehicle, since one setof movable ferromagnetic members provide both support and propulsion.

Dynamic regenerative braking is inherently a part of the system.Themotors act as generators when excited with voltage of retarded phase.

Any factor of magnetic drag such as is encountered in magnetic repulsionsystems is absent. The combined suspensive and propulsive motor providespropulsion. This, of course, is the opposite of drag.

Cryogenic apparatus for superconducting elements or elaborate conductorsin the pathway are not required; an obvious simplification.

An alternate structure, with windings in the track, provides power tooperate the vehicle through the magnetic field interacting with that ofthe motors. This arrangement makes sliding power pickups unnecessary.

A further alternate structure, with squirrel-cage conductive bars or anequivalent conductive sheet in the track, allows propulsion by theinduction motor process.

A still further alternate structure employs a uniform ferromagnetic railand attains propulsion by hysteresis in the rail.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a perspective view of onelinear motor in suspended relation to a coactive rail.

FIG. 2 is a schematic plan view of a motor, showing pluralphase windingsthereof.

FIG. 3 is a block diagram of the complete electrical system, includingmotor, sensor elements and the feedback circuit.

FIG. 4A is a schematic electrical diagram of principally the upper partof the block diagram shown in FIG. 3.

FIG. 4B is a schematic electrical diagram of principally the lower partof the block diagram shown in FIG. 3.

FIG. 5 is a graph showing the variation of voltage, current and flux vs.time as the mass (vehicle and motors) is lifted from the ground towithin the desired operating airgap between the motor and the rail, andfor maintaining the operating gap.

FIG. 6 is a graph showing the variation of voltage and frequency vs. thespeed of translation of the vehicle and motor along the rail.

FIG. 7 is a plan view of a length of an electrically active, wound,power-supplying rail.

FIG. 8 similarly shows a length of induction motor-type rail.

FIG. 9 similarly shows a length of uniform hysteresis motortype rail.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. I shows the essentials ofthe suspension and propulsion aspects of this invention. Motor 1 iscomprised of a plurality of linearly shaped magnetic qualityferromagnetic stampings similar to those employed for known rotaryelectric motors. These are held in a bundle by known means, such asbolts, not shown. A plurality of transverse slots 3 are formed in theupper part of all of the laminations. In the slots are placed aplurality of coils 4. Plural-phase electrical energy flowing in aplural-phase conductive structure is typical for this invention. Forpurposes of illustration and description three phases will be used.

Each coil may have several turns. The winding pitch is equal to the polepitch on rail 2. A pole consists of one slot and an adjacent land. Thisrepresents a successive magnetic discontinuity along the rail. In oneembodiment the pole pitch is 5 inches. The slot isconsequently 2 incheslong. Three sets of series-connected windings for phases A, B and C areprovided in the motor.

Other compromises between lifting force and propulsion force may beused. The greater the land area the greater will be the lifting force,at the expense of the propulsion force. The lifting force is one ofattraction between the motor and the rail and is energized by the sum ofthe currents in all of the coils. The propulsion force utilizes thedifference in reluctance of the paths from the motor into the railthrough the land as compared to that through a slot 5. When the currentdistribution in the three phases of coils changes because of thevariation with time of three-phase alternating current electricity, theposition of stable magnetic equilibrium is altered and the motor movescorrespondingly in order to preserve an overall path of minimumreluctance. There are three-coil slots 4 in the distance of one pole onthe rail. The coils for phases A, B, and C progress in order down thestructure of the motor.

Typically, the rail is longitudinally laminated similar to the motor andmay have the same or a somewhat reduced width. Such lamination reduceseddy current losses in the rail; thus less loss reflected into, andtherefore supplied by, the motor.

Minor variations of the rail structure may be employed. The rail may benotched or unnotched and provided with a plate of aluminum conductors tooperate as a squirrel-cage induction motor. The rail alone may be used,unnotched, and then the motor-rail combination acts as a hysteresismotor.

As is considered later, a minimum of two motors l is employed for asuspended-vehicle monorail arrangement and a minimum of four motors fora two rail vehicleover-the-rails arrangement. Suitablenonmechanicallyinterfering brackets are provided to support the rail or rails. For amonorail the vehicle may be suspended directly below the motors. For atwo rail track the motors are attached to C-shaped brackets to place themotors below the rail while the vehicle body is above the rail.

The contact between the usual railroad wheel and the railroad rail isonly a transverse line. The effective contact" between motor 1 and rail2 may be as much as 3 feet. Thus, rail 2 need be only a fraction asstiff as a railroad rail in order to carry the same load.

FIG. 2 is a schematic plan view of the upper side of motor 1, showingthe scheme of winding for the plural-phase coils.

The coils were generically indicated at4 in FIG. 1. In FIG. 2 these aresubdivided into coil 11, shown as a full line, for (11A; coil 12, shownas a dashed line, for B; and coil 13, shown as a dotted line, for C.Each of these coils may have several turns before passing down the motorframe to the next position in the slots as shown. One embodiment employs144 turns of No. 12 AWG wire for each coil. The winding scheme is of theseries type.

FIG. 3 is a block diagram of the complete electrical system, includingthe motor, sensor elements and the feedback circuit.

The feedback circuit is nonlinear in order to compensate for thenonlinearity of the motor characteristic as a function of gap length andof feedback operating frequency. At zero frequency the impedance of themotor is resistive. At relatively high frequencies for the feedbackapparatus, such as to hertz (cycles/second), the impedance is largelyinductive.

The signals from the sensor elements pass through parallel paths in partof the feedback circuit. The division between the two paths depends uponthe rapidity of the variation of the signal involved.

The resultant linearization of the feedback circuit provides a constantgain at all operating frequencies of the plural-phase power, thus at allspeeds of propulsion; and for all operative gap lengths. This maintainsa smooth ride at all vehicle speeds. Importantly, the smoothness of theride can be altered by adjustment of the feedback circuit. It is notnecessary to change the construction of the motor, or of any relatedparts of the structure.

Linearization of the voltage vs. force function for all gap lengthsallows the dynamic response of the feedback signals to be constant. Thisprovides constant stability for the system. The unidirectionalvariations of the feedback signals essentially modulate the propulsionenergy.

One sensor element 20 is an accelerometer, giving an output for anacceleration in the vertical direction as motor 1 moves up or down inspace without regard to the relationship of the motor to the rail. Theoutput thereof passes through compensating network 21 to alter thefrequency vs. amplitude response.

Another sensor element 22 is a position transducer. This gives length ofgap information. It may employ mechanical contact, or optical or sonicmeans to accomplish the measurement. The gap length is usually withinthe range of from substantially zero to one-half inches. A secondcompensating network 23 provides an adjustable reference for the gapmeasurement in electrical terms, provides amplification, anddifferentiation to give a velocity signal. Thereafter, the positionsignal is algebraically summed with the acceleration signal for commonamplification.

The attractive force between motor 1 and rail 2 is proportional to thesquare of the current passing through the coils of the motor. To providefeedback loop stability, this second order function must be linearizedby square root circuit 24, typically an operational amplifier entityemploying nonlinear transistor characteristics, to give an electricaloutput that is the equivalent of the square root of the electricalinput.

Multiplier 25 is another operational amplifier entity in which theoutput is the product, not the sum, of two electrical inputs. The outputof the square root circuit and the length of gap signal from theposition transducer are multiplied. This gives a voltage that increaseswith gap.

The electrical path through multiplier 25 is independent of frequency.Thus, an electrical output is had at zero frequency,- as for example,when the gap length is constant between motor and rail.

Perfect differentiator 26 is comprised of an amplifier having aresistance-capacitance circuit to accomplish electrical differentiation.The capacitor is not shunted by any conductive path and so the output ofthe differentiator is zero for zero frequency, that is, for DC. Thisprovides an AC path with an" output algebraically summed with that ofmultiplier 25, and gives an increasing voltage with increasing feedbackfrequency, as is required to linearize the motor response withfrequency.

The output from multiplier 25 and differentiator 26 are equal at thefrequency at which the motor DC resistance equals the motor ACreactance. At higher frequencies the motor flux is not a function ofgap.

When propulsion of anything to which motor I is attached is involved,the speed of propulsion is proportional to the frequency of theplural-phase alternating current supplied to the coils of the motor.Thus, speed control 30 is the frequency control of three-phase variablefrequency oscillator 31. What may be any number of phases from twoupward has been chosen as three phases for the example in thisspecification. The phases are typically separated by electrical degreesin time and the circuits are typically star" (i.e., Y) connected. Theoscillator must supply alternating current from zero frequency to a lowaudiofrequency at constant amplitude and of essentially sinusoidalwaveshape. An oscillator comprised of three mechanically drivensine-wave-generating potentiometers has been satisfactory in view of therelatively low frequencies involved.

The. three-phase output, A, (LB, and C, separately passes from theoscillator into three imperfect differentiators 32, 33 and 34. Thesedifferentiators are typically the series capacitor, low-valuedresistor-to-ground type ofcircuit with the addition of a relativelyhigh-valued resistor across the capacitor to give the imperfectdifferentiation. The differentiation is imperfect in that an output isprovided at zero frequency. This is required in the feedback circuit ofthis invention to overcome the resistance of the motor windings at DC,and so to provide flux in the gap between the motor and the rail. Suchflux is always required when the system is in operation, even thoughstationary, to maintain magnetic suspension of the mass, including themotor, from stationary rail 2.

Each output from imperfect differentiators 32, 33 and 34 becomes whatmay be termed the X" input to each of three multipliers 35, 36 and 37for each of the three phases. The other, or Y," input is common to eachmultiplier and is the feedback signal obtained from multiplier 25perfectdifferentiator 26 output.

Each multiplier gives the product of the instantaneous value of voltageaccording to the three-phase variation thereof by the voltage from thefeedback circuit. Thus, whether or not there is propulsion, a commoncontrol is exercised over the control signals and suspension ismaintained constant. These multipliers are of the same type as thepreviously discussed multiplier 25.

An output from each multiplier for each phase passes into controllablepower supply 38. This consists essentially of three relativelyhigh-power amplifiers, one for each phase, with the voltage output ofeach controlled according to the variation of three-phase electricalenergy with time. This includes the special case of zero frequency, atwhich the three phases each have voltages and current according to themode of threephase variation, but there is no variation thereof withtime. The particular values are frozen" in each phase until a frequencyvariation is again produced to provide propulsion.

While Class B amplifiers having an output of l kilowatt or more apiecemay be employed in a group ofthree for item 38, this amount of power isinsufficient to propulse thousands of pounds of mass, such as a largepassenger-carrying vehicle of the railroad car type. Accordingly, moreefficicnt amplifiers of higher power capabilities, such as the Class Dtype or the gated-silicon-controlled-rectifier type are employed forsuch embodiments. The basic source of power for these amplifiers is anexternal power house source 39 of three-phase power.

The relatively large power output from each-phase of controllable powersupply 38 is conveyed to the corresponding plural-phase winding of motor1, which is then attracted to rail 2 under feedback control to preventthe motor from attracting all the way to contact with the rail.

For a monorail suspended system, two motors with the complete systemshown in FIG. 3 are employed. Each motor thus properly and independentlyadjusts for uncvcncss of the track, for changes in load upon thevehicle, and for dynamic perturbations.

For a two rail system, with the rails either over the vehicle, or underit with the motor held in relation to the rail with sturdy brackets,four motors with individual control systems are employed. This gives theusual stability of a four-wheeled vehicle.

In order to equalize the stress on the rail, or to provide greatersuspension and/or propulsion capacity, more than two motors may beemployed for the monorail, or more than four motors for the birailarrangement.

FIGS. 4A and B give the complete schematic diagram for the electricalsystem of the invention and follow the technology set forth inconnection with the block diagram of FIG. 3.

Preliminary to considering the schematic diagram, the relation betweenthe electrical and magnetic parameters is given in a set of equations,since the functioning of the circuit is readily identifiable with theequations.

The magnetic force of attraction F between the motor and the rail isproportional to the square of the current I flowing through the coils ofthe motor and is inversely proportional to the square of the lengthIofthe airgap.

[" forco in grams Aren=nroa of attraction, cm l--:gap length, cm.

number of turns of coil [i=llnx density, guuss and i gall/l It)!Combining:

A1'o:tXN 1r which is Equation (1) The current I through the compleximpedance of the motor windings is, from first principles:

EE lfi-l-jwL where:

E: voltage across the impedance 1=resistanee of the coils through whichthe current is flowing j= (0 21f f frcquoncy, hertz [J -"inductance ofthe coils through which the current is flowing The inductance of a motorcoil is inversely proportional to the length ofthc airgap:

Combining and solving these equations for the voltage 1:. there isobtained:

The motors may be built in a large range of sizes, but as an example,for a 30 inch long motor capable ofsupporting 2,000 pounds, the severalconstants have the following values, with dimensions expressed ininches:

The above equations have significance in that the composition and thefunctioning of the nonlinear feedback circuit of this inventionparticularly follows equation (4), as will hereinafter be noted.

In FIG. 4A, accelerometer 20 is that described in connection with FIG.3. An essential characteristic is that it have a mass 40 of relativelyappreciable magnitude disposed to be sensitive to vertical acceleration.This plays an important part in accomplishing the easy ride" that ischaracteristic of this invention. A piezoelectric type of accelerometermay be used, such as one of the Endcvco-type 2200. The circuitry of FIG.4A does not pass the very low-frequency noise" and random variationsknown to be characteristic of this type. Altcrnately, the servo typeaccelerometer that was developed for space use and does not have thenoise and variations may be substituted for the piezoelectric type.

In the circuit of FIG. 4A amplifier entities 41, 42 and 43 .give thedetails of compensating network 21 of FIG. 3.

Amplifier 4l is a known impedance-matching amplifier and is required toreduce the very high impedance ofa piezoelectric accelerometer to anordinary circuit value. The amplifier may be a Motorola MC I456Gintegrated circuit amplifier, or an equivalent operational amplifier. Itis connected as a source-follower and has no gain, nor phase shift. Theinput circuit includes resistor 44, of 250 megohms resistance, connectedfrom amplifier terminal 3 to ground to provide an input bias currentpath for the amplifier. This is shunted by capacitor 45, of 1,000picofarads (pf.) capacitance, which acts as a padding capacitor to thestray capacitance of the input lead from the accelerometer to terminal3. The several terminals of integrated circuits, operational amplifiers,etc., have been given small numerals in FIGS. 4A and 48, correspondingto those given by the manufacturer on the device itself. The internalcircuits for these devices are known from the manufacturers catalogs.

Amplifier 41 has a feedback circuit between its terminals 6 and 2comprised of a 250 megohm resistor 46, shunted by capacitor 47, of 1,000pf. capacitance. Terminal 7 is connected to a direct current energizingpower source having a voltage of the order of volts, while terminal 4 isconnected to a similar source having the opposite polarity of 1S volts.Each of these connections is filtered by a 0.1 microfarad f) capacitorconnected therefrom to ground.

Capacitor 48, of 200 f. capacitance, is connected to the output terminal6 of amplifier 41 and is present to restrict the low-frequency signalamplitude from the accelerometer with a roll-off starting at 0.13 hertz.This removes the noise from the accelerometer circuit at lowfrequencies. Resistor 49, of 6,800 ohms, is in series with capacitor 48and with resistor 50, of 0.2 megohms, sets the accelerometer channelgain. Amplifier 42 provides an accelerometer channel gain of 200/6.8=30.The second terminal of resistor 49 connects to input terminal 2 ofamplifier 42, a Motorola MC 1741CG integrated circuit or equivalent.

There is also another input connection to terminal 2; from the output ofthe gap-length sensor circuit, to be later described.

Amplifier 42 functions as a simple amplifier, having a feedback circuitconnected between input terminal 2 and output terminal 6 comprised ofresistor 50, of 0.2 megohm, shunted by capacitor 51, of 1,500 pf. Thevoltage supply and grounding connections are standard and are known.

The accelerometer and gap-sensor algebraically summed signal now passesinto terminal 2 of amplifier 43, of MC 17416 type, through resistor 53,of 30,000 ohms resistance, which is used for gain setting. The same typeof feedback circuit is employed for amplifier 43 as was employed foramplifier 42; i.e., resistor 50' of 0.2 megohm and capacitor 55 of 0.2microfarad. Supply circuits are conventional. The output from amplifier43 is taken from terminal 6 and passes through diode 54, with thecathode thereof connected to the tenninal so that only negative signalvariations will be passed on. Additionally, diode 52 is connected as afeedback element on amplifier 43 to prevent positive voltage excursions.

Only negative voltages are allowable at the input of the square rootcircuit which follows because inversion therein to positive signalpolarity occurs before the square root function takes place. Thisprevents taking the square root of negative numbers, which areimaginary. Herein the square root circuit becomes inoperative becausefeedback of positive polarity drives it to current saturation.

We return now to the second sensor element, position transducer 22 ofFIG. 3, a device 56, which may take many forms. As shown, it is a linearpotentiometer connected to ground and shunted by a source of voltage, asbattery 57. The slider is provided with a mechanical roller. This rideson the upper side of rail 2, which is parallel with the lower oroperative side of the rail. lt is held in contact with the rail by aspring (not shown). The whole is mounted upon the structure of motor 1.

Typically, battery 57 may have a voltage of 10 volts and the travel ofthe slider of the potentiometer have a travel of onehalf inch. Thisrange of travel normally covers the operating change in the length ofthe airgap, the preferred length of which is one-fourth inch or perhapsslightly less. These constants give a voltage of times I; i.e., 20 timesthe length of the airgap as measured in inches. Battery 57 may,alternately, be a regulated power supply of the same voltage.

An alternate displacement sensor 56 may be arranged with a photocell onone side of the rail-motor gap and illumination means on the other. Asthe gap elongates, more light enters the photocell and a greaterelectrical response therefrom is obtained, while the reverse is true ofthe device if the gap narrows.

A further alternate may employ ultrasonic sound, with an electricalresponse provided by detecting the phase of the sound reflected from therail.

The output from position transducer element 22 passes to compensatingnetwork 23 of FIG. 3, which is associated with this transducer. in FIG.4A, capacitor 58, of 0.1 pf, in series with resistor 59, of 4,700 ohms,all shunted by resistor 60, of 1.5 megohms, are the initial elements ofcompensating network 23. This network has a resistive impedance of 1.5megohms from DC to 1.2 hertz, decreasing to about 4,700 ohms at 350hertz. This provides a velocity signal (i.e., differentiateddisplacement) at frequencies above 1.2 hertz.

This output passes to input terminal 2 of operational amplifier 61, anMC 1741G type as before. Both input terminals 2 and 3 of this amplifierare individually returned to ground through resistors 62 and 63, of22,000 ohms, to provide a path for the input bias currents of thisamplifier.

The feedback circuit for amplifier 61 is comprised of resistor 64,10,000 ohms, in series with capacitor 65, pf; with resistor 66, 100,000ohms, shunted across the capacitor. This gives an impedance of 110,000ohms for DC and of 10,100 ohms at 14 hertz, approximately. This resultsin the gain of amplifier 61 at frequencies below 1 hertz beingconsiderably greater than at higher frequencies. This is to increase theloop gain at low frequencies and to provide an integral of displacementfunction as a feedback signal to gradually correct for changes in load.

Since the purpose of the feedback system is to correct for changes inloading of the vehicle, wind pressure and unevenness of the track, thefrequency of the feedback signals is very low with respect to thefrequencies handled by usual electrical networks. Feedback must bemaintained at zero frequency (DC). The range of frequencies of maximuminterest extends from 0 to 5 hertz for the displacement channel and from0.3 to 30 hertz for the accelerometer channel.

Potentiometer 67, of 50,000 ohms total resistance, is connected betweenpositive and negative voltage supply sources, each of which may have avoltage of 15 volts with respect to ground. Bypass capacitors, of 50 pf,are provided from each to ground to remove extraneous variations, asknown. Potentiometer 67 provides a voltage adjustment for any initialoffset voltage in amplifier 61. The slider is connected to inputterminal 3 thereof, through isolating resistor 67 of 1.0 megohm.

An additional input to terminal 3 of amplifier 61 is from potentiometer68, of 2,000 ohms, and passes through attenuating resistor 68', of 1.5megohms, to provide a reference displacement proportional voltage.Amplifier 61 generates an output voltage proportional to the differencebetween the voltage reference input to resistor 68 and the input toresistor 60, which is the voltage from displacement transducer 22.Voltage dropping resistor 69, connected in series with potentiometer 68from the positive voltage connection to ground, typically has aresistance value half as great as the resistance value of potentiometer68.

The output of amplifier 61, from terminal 6, passes to terminal 2 inputof amplifier 42 through resistor 66', of 22,000 ohms, a summingresistor. It is at this point that compensating network 23 joins that of21, for the inclusion of amplifiers 42 and 43 in common.

The voltage output at amplifier 43 is to be treated to be linearlyproportional to a force between the load mass and the rail. Referring toequation (4), to develop the proper voltage E to be applied to the motorwindings, the force-proportional voltage is to be square rooted andmultiplied by (IR+k4'w).

The first electrical device to significantly execute the mathematics oflinearization is the square root circuit identified as 24 in FIG. 3 andas 24'-70 in FIG. 4A. This may be a Motorola integrated circuit MCl494L, normally known as a multiplier" of electrical signals fed intoit. This is placed in the feedback circuit of an operational amplifierand the square root of the single input provided is obtained.

The theory and practice of this square root performance is known, beingset forth in the (Motorola) manufacturers, Specifications andApplications Information," Get. I970DS 9l63. In FIG. 4A herein theoperational amplifier required is identified as 70, and may be an MCl74lG integrated circuit.

In FIG. 4A, the output from the previously mentioned diode 54 isconnected to gain-setting resistor 71, of 52,000 ohms, and also toground through resistor 72, of 1,000 ohms. The latter resistor providesa path for any leakage current in diode 54. The input from resistor 71is connected to terminal 14 of multiplier 24' and also to terminal 2 ofamplifier 70. The output of this amplifier, at terminal 6, is connectedto terminals 9 and of the multiplier and also to ground by a smallcapacitor 73, of 10 pf. capacitance, in series with resistor 74, of 510ohms. Zener diode 75 is also connected between the output of amplifier70 and ground to prevent accidental latchup (malfunctioning) of thecircuit. A type 1N524l may be used.

The feedback path for amplifier 70 is the multiplier 24 connectedbetween input terminal 2 and output terminal 6 of amplifier 70 andterminals 9-l0 and 14 of the multiplier. Capacitor 76, of IO pf.capacitance, and connected between amplifier terminals 2 and 6 is forthe purpose of phase-compensating the amplifier. Input terminal 3thereof is connected to the slider of potentiometer 77, whichpotentiometer has a resistance of 20,000 ohms. This provides a voltagereference for the amplifier. This potentiometer is connected in parallelwith a duplicate potentiometer 78, which is connected between terminals2 and 4 of multiplier 24'. Also associated with multiplier 24', resistor79, 62,000 ohms, is connected between terminals 7 and 8; resistor 80,30,000 ohms, is connected between terminals 11 and 12; and resistor 81,16,000 ohms, is connected between terminal 1 and ground. A voltagesource, typically of 15 volts, of positive polarity is connected toterminal 7 of the amplifier and terminal 15 of the multiplier, whereas avoltage source, typically of 15 volts, of negative polarity is connectedto terminals 4 and 5, respectively.

At the input to the whole square root circuit 24 of FIG. 3, a negativesignal voltage of 4 volts produces in the whole system a force of l g.That is, an equal and opposite force in relation to that of gravity, andso the motor vehicle mass is magnetically suspended. With theconnections and voltages given, the output of the square rooter atterminal 6 of amplifier 70 is the square root of [0 times the input.This is the square root of 10 in efiective amount and is taken intoconsideration in establishing the whole feedback gain. Mathematically,such functioning of the electrical circuits is accounted for in thevalues of the several k constants.

The output from the square root circuit is connected to the input ofmultiplier 25 to perform the IR portion of equation (4), and also to theinput of perfect differentiator 26 to perform the k jw term, as seen inFIG. 3. In FIG. 4A the input to multiplier 25 is terminal 10 thereon andto the perfect differentiator is capacitor 83 through resistor 90.

The above input to the multiplier may be termed the .r" input. The y"input is connected to input terminal 9 and comes directly from positionsensor 22 (56 being one embodiment) through resistor 84 for isolation.The resistance value of resistor 84 may be 0.1 megohm. Both inputterminals 10 and 9 are also connected to ground through capacitors 85and 85, of 10 pt capacitance, in series with resistors 86 and 86, of 510ohms resistance, respectively. These prevent high-frequency parasiticoscillations.

Resistors 79', 80, and 81' are identical in resistance value andconnection to multiplier unit 25' as these were with respect to unit24'. So also are potentiometers 77 and 78', except that the resistancevalue of potentiometer 77 is 50,000 ohms. An additional potentiometer87, of 20,000 ohms, is connected across terminals 2 and 4 of units 25,with the slider connected to terminal 6. These three potentiometers aread- LII justed to give proper x, y" and output offset bias, as out linedin the manufacturers Specification and Application Informationpreviously referred to.

An MC l74lG operational amplifier 89 coacts with multiplier unit 25 togive the complete multiplier 25 of FIG. 3. Feedback capacitor 76', of 10pf, is connected to the amplifier at terminals 2 and 6, and is shuntedby resistor 88, of 52,000 ohms. Positive and negative voltage supplysources are as before.

Perfect differentiator capacitor 83 has a capacitance of 0.2 p.f. It isin series with resistor 90, of 1,000 ohms resistance. The capacitorconnects to input terminal 2 of operational amplifier 91, which may be aMC l741G type. The feedback circuit of this amplifier is comprised ofcapacitor 92, 0.0068 pf, and resistor 93, 0.1 megohm, in parallel andconnected between amplifier terminals 2 and 6. Second input terminal 3is grounded. Positive power supply voltage is connected to terminal 7,while the same in negative polarity is connected to terminal 4. Thisamplifier-differentiator provides the first derivative of the input overa frequency range of from essentially zero to 200 hertz.

The output from amplifier 91 is taken through summing resistor 94,62,000 ohms, to input terminal 2 of amplifier 95. The latter mainlyraises the signal level, after providing for the summing, for parallelfeeding all of the three-phase multipliers that follow.

Similarly, the output from multiplier operational amplifier 89 is takenthrough summing resistor 94', 62,000 ohms, and connects to inputterminal 2 of amplifier 95. This provides the total electricalrepresentation of F(lR+k iw) of equation (4).

The feedback circuit 92, 93' of amplifier 95 is the same as the feedbackcircuit 92, 93 of amplifier 91; also, input terminal 3 is connected toground and the power supply connections are the same as before.

The output at terminal 6 of amplifier 95 passes to potentiometer 96, thesecond terminal of which is connected to ground. The slider of thepotentiometer is connected to all terminals 9 of the three multipliers35', 36, and 37' of FIG. 4B. These multipliers are the essential unitsof the three multipliers 35, 36 and 37 of FIG. 3. The accompanyingoperational amplifiers in FIG. 4B are 97, 98 and 99, respectively.

This single control feedback input performs the function of maintainingsuspension with or without propulsion and regardless of what theindividual voltages in phases A, B and C might be at any instant of timeaccording to the inherent variation of three-phase electric power. Thecombined gains of potentiometer 96, multipliers 35, 36 and 37, and thevoltage gain of controllable power supply 38 determines k l in equation(4) so that 4 volts of signal at the input of square rooter 24 is l g.

Adjustment of the suspension gap length I is accomplished by varying thevoltage at the input 3 of amplifier 61, as determined by the setting ofpotentiometer 68, of FIG. 4A.

In FIG. 4B the common control from the feedback circuit is identified byY." An individual phase input is also provided. Phase A is connected toterminal 10 of multiplier unit 35.

The internal and external connections of unit 35 and of its accompanyingoperational amplifier are all the same as previously detailed formultiplier-amplifier 25 -89 of FIG. 4A, and so will not be repeated. Thephase inputs for the three multipliers arise in three-phase oscillator31, to be later described. The output from terminal 6 of amplifier 97 isconnected to 41A of controllable power supply of FIG. 3 identified as38. This is represented as the input to power amplifier 108 in FIG. 4B.

In the same manner, multiplier 36 98 handles (#8, and multiplier 37'99handles C.

Devices relating to the propulsion and the connections thereof to theabove multipliers are also detailed in FIG. 43.

Speed control 30 is schematically shown as a rotatable (dotted line)shaft attached to the sliders of each of potentiometers 101, I02 and103. These potentiometers are preferably wound to provide a sinusoidalvariation of voltage with motion of the sliders, are of circularconfiguration, and are suited for full and repeated rotation of thesliders. Each slider is attached to the shaft at l20electrical degreesfrom the others, in usual three-phase fashion. The potentiometerscomprise three-phase variable frequency oscillator 31. These areelectrically connected in parallel, at one extremity to a source ofpositive supply voltage, such as volts, and at the other extremity to asource of negative supply voltage, also 15 volts.

For testing, shaft 30 can be revolved by hand. For commercial use it canbe revolved by a geared-down variable speed motor. The speed control onthe motor becomes the manually operated speed control, to be adjusted bythe driver of the vehicle. It is desirable to limit the accelerationinvolved in moving the vehicle down the track to one-tenth g; i.e.,onetenth that of the acceleration due to gravity. This can be controlledby arranging a dashpot-type element attached to the speed control on themotor so that sudden speed changes are not possible.

Another suitable oscillator is the function generator, type120-020-manufactured by the Wavetek company of San Diego, Calif.

One imperfect difierentiator, 32, 33 or 34, is connected to each phaseoutput from oscillator 31. Considering imperfect differentiator 32;capacitor 104, of pf. capacitance, is connected to the slider onpotentiometer 103 and also to resistor 105, the latter having therelatively small value of 1,000 ohms. The second ten'ninal of theresistor is connected to ground.

As was explained in connection with FIG. 3, an output at DC is requiredof these differentiators. Resistorl 06, of 10,000 ohms, is connected inshunt to capacitor 104 to provide such an output and cause thedifferentiators to be of the imperfect type. The output is taken at theconnection between elements 104 and 105 for 42A. The structure forimperfect differentiators 33 and 34 is identical to that of 32, and sowill not be detailed.

Controllable power supply 38 has already been described in connectionwith FIG. 3 as comprised of three high-power amplifiers. Class Bamplifiers and the circuit diagram for the same are well known. The samefor a Class D amplifier, a recognized IEEE designation, is availablecommercially from TRW Semiconductors, Inc., Lawndale, Calif: their typeMCB 1002. A similar variable pulse-width switching-type amplifier butwhich uses silicon-controlled-rectifiers instead of power transistors,is available from the Gates Learjet Corp., Irvine, Calif.

In FIG. 48 these amplifiers are shown as I08, 109 and 110, for phases A,B, and C, respectively. Each amplifier provides an output to acorresponding winding 111, 1.12 and 113 of suspension and propulsionmotor I, also shown. Each amplifier is indivicb ally fed from acorresponding multiplier 35, 36 or 37. In FIG. 48, these multiplierstenninate in amplifiers 97, 98 and 99, respectively, which may beintegrated circuits.

Typically, 220 volt three-phase electric power is supplied to eachamplifier 108, 109 and 110 from a stationary source of power 39, such asa power house. It reaches the amplifiers through a plural conductor 3rdrail 39, with which plural contacts carried by the vehicle make contact.Each amplifier may accordingly include a three-phase rectifier toprovide the DC energizing power as is usually required. In an alternatearrangement, direct current is directly supplied to the vehicle by asingle 3rd rail.

The circuit of FIGS. 4A and 4B is for one motor 1 (as is furtherillustrated in FIGS. 1 and 3). With this arrangement, each of the pluralmotors usually required for a vehicle has its own sensor means andfeedback control circuit for superior response to variations broughtabout by unevenness of track, etc.

The motors may be built in a wide range of sizes; however, a length offrom 15 to 30 inches and a width of motor and rail of the order of 3inches is typical. For a 30 inch three-phase motor, the weight is 125pounds. When excited it can suspend 2,000 pounds. When it is suspendingonly, the vehicle being at rest, 400 watts per phase of power isconsumed and the kilovolt-ampere wattless power has the same value. Asthe motor provides propulsiz e force the kilovolt-amperes increases at afaster rate than does the wattage loss. At miles per hour and fullthrust these values are 80 KVA and 25 KW per motor, respectively, asdetermined by exterpolating motor impedance measurements.

The performance of the feedback circuit of this invention is maintaininga constant length of airgap between motor and rail is believed toprovide significant functioning required for practicalmagnetic-supported transportation; functioning which has hitherto beenunknown or unexplained.

The force exerted magnetically by the motor in providing suspensionvaries as the square of the current in the windings of the motor. Thisis a nonlinear relation. Nonlinear elements in the feedback circuit,such as the square root circuit 151 of FIG. 3, make the output of thefeedback circuit linear, from a voltage input to a force output. Thisresults in a constant feedback loop gain at all values of alternatingcurrent frequency (speed of the ehicle) and at all gap lengths of themotor to the rail. Moreover, this results in a uniform easiness of ride.A typical variation of gap may extend from +100 percent to nearly l00percent of a normal value of one-fourth inch. To prevent the motor fromactually contacting the rail, a flat automotive-type brake shoe may bearranged to bear upon the rail instead, as a safety measure.

Because an inertial reference, accelerometer 20, is used in the verticalplane, the feedback circuit ignores small track irregularities and doesnot pass them on to the passengers in the form of vibration or quickjolts. Only a mean gap is maintained by the displacement (position)transducer2 2. Prior systems, suggesting known solidirlrfeedback, dopass on all track irregularities to the passengers.

It has been found that the attractive type suspension system withnonlinear feedback according to this invention exhibits damped lateralstability. This is economical of weight required to be carried for theinherent operation of the vehicle. Each motor L provides suspension,propulsion and lateral stability. Experimentally, a perturbation pushingthe motor sideways with respect to rail 2 causes the current to increasethrough the amplifiers of controllable power supply 38, which acts tokeep the gap length constant. A restoring force is noted, laterally,which increases with lateral displacement.

Upon the perturbative lateral force being removed. the motor returns toan aligned position with the rail in a damped manner, and does notovershoot. The damping arises from two factors; the resistance of thecoils in the motor windings, and a back electromotive force created inthe windings by the lateral displacement. The energy represented by thefonner is dissipated in the resistance of the coils, and by the latteris restored to the power mains through controllable power supply 38 bygenerator action.

Preferably, the width of the magnetic structure of motor I is at least10 percent greater than the magnetic structure of the rail 2 forvigorous lateral stability. It is to be noted that lateral stability isnot inherent in a repulsive magnetic support system, witha motor over arail. In such a system an auxiliary magnetic motor or'mechanical rollersare required, to act laterally against the rail.

The feedback loop that includes accelerometer 20 makes a second ordercorrection to the overall feedback network. This is about 10 db offeedback rwer the frequencies of interest, from one-half to 5 hertz.This makes the system insensitive to second order variations: such asvariations in the magnet structure of a motor I, as may be encounteredin practical construction, the AC resistance of a coil thereof, thechange of coil resistance with temperature, as well as variations of theDC gain and of the AC gain of the feedback network. The second ordercorrection also prevents instability at certain gap lengths.

The prior art does not appear to have discussed these matters, which areof significance in providing an inherently stable transportation systemdespite day to day variations in parameters. weather, and otherpractical matters, including the capability of smoothly handling gapvariations caused by rough rail alignment. I

Considering operative details of a typical embodiment for thetransportation of people, the gain of amplifier 41 of FIG. 4A is, ofcourse, unity. The gain of amplifier 42 is approximately 30, up to anupper cutoff frequency of 8 hertz. The gain of amplifier 43 isapproximately 7, with an upper cutoff frequency of 4 hertz. When theoutput of this amplifier is 4 volts, the force exerted by motor I is lg.; i.e., the vehicle is suspended.

In forming the feedback circuits according to this invention use is madeof the fact that the AC fiux density in the motor to rail airgap doesnot vary if the length of the gapchanges This flux density is affectedonly by the value of the volts-per-tum in the magnetic structure, and sothe voltage only in any given magnetic structure. Multiplier 25 of FIG.3 provides compensation for DC flux density changes with changes in thelength of the airgap. Position transducer element 22 senses the DC gaplength and the gain of the feedback circuit is modulated to increasewith gap length, maintaining the overall system gain, including thecharacteristics of motor 1, constant.

In a typical motor the inductive reactance of the coils is equal to theresistance of the coils at a frequency of the order of 2 hertz. Theinductance does vary inversely with the length of the airgap, but properfeedback performance is maintained by having the DC path throughmultiplier 25 and the AC path through perfect differentiator 26. Theexciting current through the motor coils increases with gap length, thusthe DC flux remains constant.

In practical operation, this necessary mode of operation requires thatextended periods of suspension at long airgaps cannot be allowed. It isgood practice to rate the amplifiers comprising controlled power supply38 for the average length of gap encountered and to return the vehicleto that length within a few seconds without causing an artificial joltafter a gap-lengthening perturbation.

Capacitor 55, of 0.2 pf. capacitance, FIG. 4A, which is connectedbetween output terminal 6 and input terminal 2 of amplifier 43, acts asa partial integrator upon the acceleration feedback signal. Thisprovides a quasivelocity feedback signal and prevents an oscillatorycondition otherwise existing because of an 180 phase shift betweenacceleration and displacement. This is effective from a frequency of theorder of IO hertz down to 4 hertz.

Below 4 hertz differentiation of the position (displacement) feedbackoccurs to provide the velocity component. This is produced by capacitor58 in the input circuit to amplifier 61, shown in FIG. 4A.

The combination of these two signals gives control of the phase of thefeedback circuit so that displacement information can be fed into asystem that has feedback from an accelerometer included in it. Actually,four aspects of feedback are present in the system to give a high degreeof stability; the integral of displacement to bring the system back to amean gap length after load changes in the vehicle, displacement feedbackto stabilize the integral displacement feedback circuit, velocityfeedback to stabilize and damp the displacement feedback, andacceleration feedback to stabilize and damp the velocity feedback. Atthe same time the acceleration feedback corrects second ordernonlinearities in the linearizing acceleration circuit comprised ofsquare rooter 24, multiplier 25, and differentiator 26 in FIG. 3.

Acceleration and force are synonymous in equation (4). Theabove-described mode of operation is required for any system of thenature of a magnetically supported railroad, where the airgap length ispurposely allowed to vary to accommodate rough track. The gap is broughtback to a mean value gradually, to provide a soft ride.

FIG. shows the variation of the several parameters involved in liftingthe motor (and vehicle) from the ground toward a rail and maintainingthe airgap between the motor and the rail at a prescribed length.

The vehicle is to be raised a distance d to reduce the airgap length Itoa desired value s. This value may be of the order of one-fourth inch fora railway-type vehicle. No forward motion of the vehicle is assumed inFIG. 5; the process being considered is for establishing magneticsuspension of the vehicle.

In the graph the abscissa is time and the ordinate has various values,as will be evident.

At time equals zero; i.e., the start of the lifting process, the voltageis impressed upon the coil windings of the motor. It rises to a highsaturation level, as shown at 115. Thecorresponding current ll6 in thewindings involved starts with a zero value at time equals zero andincreases as a ramp function until time t,, at which time an upwardvelocity of the vehicle toward the rail starts. The magnetic fluxproduced by the motor and extending into the rail increases as thecurrent increases and so this is a companion ramp function, shown as 117in FIG. 5.

As soon as an upward velocity of the vehicle starts an accelerationexists and this is sensed by the accelerometer. Through the feedbackcircuit that has been described the accelerometer signal reduces theapplied voltage to zero; actually to a small negative value as shown.This allows the up ward velocity to be controlled. After an initialvalue of zero at time t, it reaches a maximum value at a later time t atand after which time the upward velocity is decreased.

Displacement curve 118 starts from zero at time t, and increasespositively, but at a slower rate than the previously mentioned velocitycurve 119. The proper value of feedback signal causes the displacementcurve to cease changing with time after a time t, is reached. Thissignifies attainment of the preselected gap length. At time i velocitycurve 119 has decreased to zero. The desired vertical position has beenachieved. At time the length of the airgap has decreased from theinitial value. Less current 116 is thus required to maintain the neededflux and so this parameter remains constant with time at a value lessthan that existing at time t,.

Flux curve 117 remains at a constant value with respect to time fromtime t, to about half-way between time t, and t The flux is then reducedto a value less than that required to support the weight of the vehicle.This causes the upward velocity of the vehicle to be reduced, thusproducing a negative acceleration, or deceleration.

The prior negative value of applied voltage reverses as the otherparameters reach equilibrium shortly before time t;,. After time itremains at a relatively small positive value that is sufficient to causecurrent 116 to flow at an amplitude to maintain flux 117 at a constantvalue.

By time t; has been reached the airgap has been reduced to thepreselected value of s. It remains at that value unless there beexternal factors acting to change it. If such factors tend to increasethe gap length the same variation of the several parameters aspreviously described occurs and the gap length is reduced to thepreselected value. If such factors tend to decrease the gap length theseveral parameters vary in the opposite manner.

FIG. 6 is a graph showing the variation of essential electricalparameters with horizontal velocity of a vehicle attached to a motor.The vertical aspects of the electrical characteristics of the motor areassumed to be established, as after time I in FIG. 5, and that these donot vary. Should there be a vertical variation at the same time that thevehicle is moving, as due to uneven track or a change in load, then theactual variation of the parameters is a combination of the variations onboth graphs.

In FIG. 6 it will be noted that the value of magnetic flux 121 isconstant at all values of horizontal velocity. This condition ismaintained by the operation of the feedback circuit of FIG. 3.

The velocity of the vehicle increases as a direct function of frequency122 of the plural-phase alternating current flowing in the plural-phasewindings of motor 1. Thus, it is represented by a straight line ofpositive slope that passes through the origin of the graph. The higherthe frequency the more rapidly the position of stable magneticequilibrium moves along the linear extent of the motor, thus the morerapidly motor 1 moves with respect to the stationary rail (track) 2.

Because the motor-gap-rail assembly is a magnetic structure largely ofthe ferromagnetic type, it makes a considerable contribution to theinductance of the plural-phase windings. The impedance of the windingsthus increases with frequency because of the increase of inductivereactance. Voltage relation 115' as a function of speed of the vehicleis thus defined by a straight line of positive slope directed toward theorigin and having a slope determined by the value of the inductance ofthe windings as used in the suspension and propulsion mode. Anasymptotic approach to this straight line of voltage 115 occurs up fromthe origin (above it) near the zero velocity abscissa because of the DCresistance of the motor windings. See also FIG. 5, the voltage valueafter Imperfect differentiators 32, 33, 34 act to produce curve 115';keeping current constant.

FIG. 7 shows a section of a wound rail. One or more such rails may beemployed in an alternate method and structure of this invention forfeeding power to the motors of the vehicle by means of what can betermed the amplidyne principle.

A modified rail 2', which may be longitudinally laminated for high speedtransportation use, is provided with uniformly spaced transverse slots110 on its lower face. This face is shown upward in FIG. 7 for clarity.

Plural coils carrying plural phases of alternating current electricpower are shown schematically wound in the numerous slots 110. In FIG.7, three phases are shown, coil 111 for 41A in full lines, coil 112 for(1:8 in dashed lines, and coil 113 for dzC in dotted lines. Each coilmay have more than one turn in the slot shown, before passing down therail to the next coil configuration.

This rail is employed with the three-phase wound motor shown in FIGS. 1and 2. The motor-wound-rail system is operated so that the alternatingcurrent frequency of current flowing in the rail coils is different fromthat required in the motor coils for propulsion. propulsion. This isaccomplished by providing sufficient leading power factor elements as anelectrical load on the vehicle-mounted motor. Capacitors are employed tocause the power factor of the motor to be leadmg.

Under these conditions the wound portion of motor 1 has an alternatingcurrent of low frequency in it, rather than an induced direct current,as would be the case for synchronous operation. The coils in the railact as the primary of an energyfumishing transformer, of which the coilsin the motor are the secondary. The transfer of energy to the mot0r(s)of the vehicle is sufficient to provide the suspension current therein,and an excess for air conditioning, lights, etc., in the vehicle. Therail may be considered the wound armature and the motor coils as thefield of a wound-rotor wound-stator reluctance motor.

A 3rd-rail type of power pickup is not required.

FlG. 8 shows an induction motor-type rail. It is the equivalent of thesquirrel-cage rotor of the usual rotary type induction motor.

The rail 2", which may be assembled of longitudinally laminated stripsof ferromagnetic material for high speed transportation use, is providedwith uniformly spaced transverse slots on its lower face. This face isupward in FIG. 8, for clarity of illustration. The slots are spaced thesame distance as the slots containing the windings of motor 1, as seenin FIG. 2.

Each slot is provided with a relatively highly conductive material, suchas aluminum, 115, which is bonded to the socalled shorting bar 116 and117 on each side of the rail. Typically, the slots are one-halfinch deepby one-halfinch wide for a 3 inch wide rail. The aluminum material maybe formed in a long cutout strip and forced into the slots in the railper se. This construction provides repetitive electricaldiscontinuities.

This motor-rail combination functions in the same manner as the knownrotary induction motor. The relative motion between motor and track isslower than synchronous speed. The consequent moving magnetic fluxpassing through the aluminum winding" in the rail slots producescirculating currents in the slot-shorting-bar structure. The magneticfield created by these currents then interacts with the flux from motor1 and a propulsive force is produced.

The induction-type rail may be simplified by merely providing analuminum sheet on the underside of the ferromagnetic rail as it isoriented in use. Therein the circulating currents mentioned above areinduced upon slip occurring. These find their own paths in the aluminumsheet, giving the required interacting flux. This is a simple alternateembodiment, but results in a reduced mechanical gap for clearancebetween the motor and the rail.

FIG. 9 shows a length of uniform hysteresis motor-type rail 2". This maybe the top surface of the known steel rail of ex isting railroads,should the propulsion aspect of this invention be employed without thesuspension aspect. Otherwise, the drawing represents the bottom surfaceof a rail suspended so that motor 1 of this invention may also besuspended below it for the suspension and propulsion ofa vehicle. Therail is magnetically homogeneous.

In addition to steel as a material for this rail certain ferrites, suchas Ferroxcube Corp. Type 387, may be used. For the purposes of thisinvention the hysteresis loop of the rail material is preferablyrectangular, which gives maximum thrust during the demagnetizationcycle. For the hysteresis mode of operation the rail becomes magnetizedto some degree in the nature of a permanent magnet. This magneticallyinteracts with the magnetic field of motor 1.

Referring to FIGS. 4A and B as to operation, when the suspension systemof the vehicle is inactive and it is resting on physical supports, notshown, which are provided on the railway; to activate the suspensionsystem and properly relate the motors l to rail 2, electric power from 3rb power (supply) 39 is applied to power amplifiers 108, 109 and 110 andthe several power sources indicated as and are energized.

The slider of potentiometer 68 is adjusted to apply a reference voltageto terminal 3 of amplifier 61 equal to the voltage required at terminal2 of amplifier 61 to lift the vehicle to the desired length of gap fromrail 2.

The feedback system then increases the current from power amplifiers108, 109 and 110 through windings 111, 112 and 113 in motor 1 causingthe motor and attached mass to rise.

Position transducer 22 senses the consequent length of gap and causesthe voltage at terminal 2 of amplifier 61 to equal that at terminal 3when the desired length is reached.

Regenerative braking may be employed with the systems of this invention.To accomplish this motor windings 11, 12 and 13 are provided with avoltage at a phase retarded from that of the frequency corresponding tothe velocity of the vehicle. The more this phase angle is retarded thegreater is the braking force. The theoretical maximum retardation iselectrical degrees.

An alternative acceleration feedback signal may be used instead of thatfrom inertial-reference accelerometer 20. This is an acceleration signalderived from the relative acceleration of the mass (including motor 1)with respect to rail 2. Such a signal may be produced by a flux-sensingdevice in the magnetic circuit, such as a Hall-effect transducer. Thisis substituted for accelerometer 20 in the circuit.

This signal will not provide isolation of the mass from irregularitiesof the rail, but might be useful where the vehicle is to follow the railquite closely for technical reasons, or where the greater cost of aninertial accelerometer is to be avoided.

Herein, specific circuit values, specific number of phases, and otherspecific data have been set forth for sake of clarity. However, specificcircuit values may be altered by at least plus or minus 20 percent. Theelectrical equivalents of the integrated circuits and operationalamplifiers may be used regardless of their size or other peripheralfeatures.

Also, various ratios of feedback from the inertial (accelerometer)reference compared to gap-sensing reference lclaim: l. The method ofsuspending and moving a mass which includes the steps of;

a. magnetically attracting said mass toward a a stationary element inthe direction opposite to the direction of the attraction due to gravityto define a gap therebetween,

b. regulating the magnitude of the magnetic attraction exerted upon saidmass by nonlinear electrical feedback related to the attracted positionof the mass, and

c. electrically altering the magnetic configuration associated with saidmass transverse to the direction of attraction due to gravity tolongitudinally move the position of stable magnetic equilibrium for saidmass with respect to said stationary element.

2. The method of claim 1 in which;

a. the magnitude of magnetic attraction is regulated by sensing thevertical position of the mass and the acceleration of change of thatposition.

3. The method of claim 1 in which;

a. the magnetic configuration is altered by changing the magnetizationof at least a part of said mass by passing plural-phase alternatingelectric current through it.

4. The method of claim 1 in which;

a. the alternating current feedback gain of said electrical feedback issubstantially constant as a function of the attracted position of themass.

5. The method of claim 3, including the step of;

a. controlling the amplitude of said plural-phase alternating current asa function of its frequency, whereby the feedback gain may be maintainedsubstantially constant notwithstanding changes in the frequency.

6. The method of claim 1, including the additional step of;

a. regulating the magnitude of the magnetic attraction exerted upon saidmass by control of said nonlinear feedback to provide lateral stabilityof said mass with respect to said stationary element.

7. Magnetic suspension apparatus comprising;

a. a stationary ferromagnetic member (2),

b. a movable ferromagnetic member (1), disposed below said stationarymember and defining a gap between said members,

c. an electrical circuit (4, 38) associated with said movable member toproduce a magnetic flux across said gap,

d. a first sensor element (22) responsive to the length of said gap,

e. a second sensor element (20) responsive to motion of said movablemember, and

a nonlinear feedback circuit (24, 26) including said first and secondsensor elements and connected to said electrical circuit for theelectrical control of said electrical circuit over a wide range oflength of said gap.

8. The apparatus of claim 7 in which;

a. the magnetic flux across said gap is developed by alternating currentapplied to said electrical circuit, and

b. the output of said feedback circuit is a direct current controlvoltage i to control the magnitude of said alternating current.

9. The apparatus of claim 8 in which;

a. said stationary member is an elongated rail, and

b. said movable member includes means to shift the position of stableequilibrium along said rail.

10. The apparatus of claim 7, in which;

a, said stationary ferromagnetic member is a rail having repetitivemagnetic discontinuities, and

b. said electrical circuit has plural paths (l1, l2, 13) to carryplural-phase electric current to progressively alter the position ofstable magnetic equilibrium of said movable member with respect to saidrail for translating said movable member (I) along said rail. 11. Theapparatus of claim 10 in which; a. said electrical circuit is wound (ll,l2, 13) for plural phases of electricity, and b. said magneticdiscontinuities are spaced to include a part of said electrical circuitwhich carries all of said plural phases. 12. The apparatus of claim 10in which; a. the plurality of the plural-phase paths of said electricalcircuit is three. 13. The apparatus of claim 7 in which; a. saidstationary ferromagnetic member is a rail having discrete repetitiveelectrical paths, and b. said electrical circuit has plural paths (ll,l2. 13) to carry plural-phase electric current, to induce electriccurrent in said electrical paths for progressively altering the positionof stable magnetic equilibrium of said movable member (1) with respectto said rail to translate said movable member along said rail. 14. Theapparatus of claim 13 which includes; a. electrical discontinuityconductors transverse to aid rail, and b. longitudinal shortingconductors (116, 117), the electrical conductivity of said conductorsand said shorting conductors being greater than the transverseelectrical con ductivity of said rail. 15. The apparatus of claim 7,which additionally includes; a. a uniform electrical conductor (2"')substantially coextensive with and attached to the underside of saidstationary ferromagnetic member (2) to lie within said gap, whereby saidmagnetic flux induces electric currents in said unifonn electricalconductor to magnetically propel said movable ferromagnetic member (1)along said stationary ferromagnetic member. 16. The apparatus of claim7, which additionally includes; a. further plural-phase windings (11 l,112, 113) repetitively disposed along said stationary elongatedferromagnetic member (2), b. means to energize said further plural-phasewindings with plural-phase electric current, and c. electricallyreactive means to alter the phase of electric current flowing in saidelectrical circuit (4, 38) by induction from said further plural-phasewindings from the phase of the electric current flowing in said furtherplural-phase windings,

whereby electric power is transmitted from said further plural-phasewindings to said electrical circuit.

17. The apparatus of claim 7 in which;

a. said stationary ferromagnetic member (2) is magnetically uniform andhomogeneous, is magnetically retentive, and exhibits magnetichysteresis, whereby a longitudinal force is exerted upon said motor (1)upon electric current flowing through the electric circuit thereof.

18. The apparatus of claim 7 in which;

a. said movable ferromagnetic member (1) is longitudinally laminated.

19. The apparatus of claim 7 in which a. said stationary ferromagneticmember (2) is longitudinally laminated.

20. The apparatus of claim 7, in which said nonlinear feedback circuitincludes;

back circuit includes;

a. another electrical element (26) having an electrical outputproportional to a mathematical differential of the electrical inputthereto.

22. The apparatus of claim 7, in which the nonlinear feedback circuitincludes;

a. an electrical integrator (58, 59, 61) connected to said first sensorelement (22) responsive to the length of the p b. said integrator andalso said second sensor element (20) responsive to accelerationconnected to a first electrical element (24) having an electrical outputproportional to a mathematical root of the electrical input thereto,

c. the electrical output of said root element connected to a secondelectrical element (26) having an electrical output proportional to themathematical differential of the electrical input thereto, and

d. the output of said second electrical element connected to saidelectrical circuit (35, 36, 37, 38 4) associated with said movableferromagnetic member (1) for the control of said electrical circuit.

23. The apparatus of claim'7, in which said electrical circuit includes;

a. a variable frequency plural-phase oscillator (31) to originatealternating electrical energy for energizing said electrical circuit(38, 4)

at a selected frequency corresponding to the desired velocity oftranslation of said movable ferromagnetic member 1).

24. The apparatus of claim 23, in which said electrical circuitadditionally includes;

a. an imperfect differentiator (32, 33 or 34) connected to each outputphase circuit if said plural-phase oscillator and to said electricalcircuit (38, 4), to give an increasing voltage output with increasingfrequency for overcoming the inductive reactance of said electricalcircuit (4) associated with said movable ferromagnetic member (1).

25. The apparatus of claim 23, in which said electrical circuitadditionally includes;

a. plural electrical multipliers (35, 36, 37), each having,

b. a first input circuit (A, B, C) connected to an output phase circuitofsaid plural-phase oscillator (31),

c. a second input circuit (Y) connected to said nonlinear feedbackcircuit, and

d. an output circuit connected to said electrical circuit (38,

for energizing said electrical circuit proportional to the product ofthe electrical amplitudes derived from both said oscillator and saidfeedback circuit.

26. Magnetic suspension apparatus comprising;

a. alternating current energized electromagnetic means for freelysuspending a mass by magnetic attraction against the force of gravityacting thereon,

b. sensing means carried by the mass for sensing movements thereof awayfrom a reference position, and

c. feedback means including said sensing means for regulating themagnitude of the alternating current energization in accordance withmovements sensed by the sensing means to thereby restore the mass to itsreference position over a range of frequency upwards from zero.

27. The apparatus of claim 26 wherein;

a. the feedback means generates a direct current feedback voltage forcontrol of the magnitude of the alternating current energizationcurrents.

28. The apparatus of claim 27 wherein;

a. said feedback voltage includes a control parameter to compensate forchanges in the total weight of said mass to thereby restore the same tosaid reference position notwithstanding said changes in weight.

29. The apparatus of claim 27 wherein;

a. the feedback voltage includes a control parameter res onsive to thevelocity of movement of the mass. 30. e apparatus of claim 27 wherein;

a. the feedback voltage includes a control parameter responsive to theacceleration of movement of the mass.

31. The apparatus of claim 27 wherein;

a. the feedback voltage includes a control parameter responsive to thedisplacement of the object from its reference position.

32. The apparatus of claim 27 wherein;

a. the feedback voltage in response to said movements varies as theproduct of displacement of the mass from said reference position timesthe algebraic sum of l. the integral of said displacement,

2. said displacement, 3. the velocity of said movements, and 4. theacceleration of said movements.

33. The apparatus of claim 32 wherein;

a. said displacement is a dominant factor affecting the feedback voltagewhen the frequency of changes in displacement is in the range from DC to1.2 hertz.

34. The apparatus of claim 32 wherein;

a. said acceleration is a dominant factor affecting the feedback voltagewhen the frequency of changes in said displacement is in the range abovel.2 hertz.

1. The method of suspending and moving a mass which includes the stepsof; a. magnetically attracting said mass toward a stationary element inthe direction opposite to the direction of the attraction due to gravityto define a gap therebetween, b. regulating the magnitude of themagnetic attraction exerted upon said mass by nonlinear electricalfeedback related to the attracted position of the mass, and c.electrically altering the magnetic configuration associated with saidmass transverse to the direction of attraction due to gravity tolongitudinally move the position of stable magnetic equilibrium for saidmass with respect to said stationary element.
 2. said displacement, 2.The method of claim 1 in which; a. the magnitude of magnetic attractionis regulated by sensing the vertical position of the mass and theacceleration of change of that position.
 3. The method of claim 1 inwhich; a. the magnetic configuration is altered by changing themagnetization of at least a part of said mass by passing plural-phasealternating electric current through it.
 3. the velocity of saidmovements, and
 4. the acceleration of said movements.
 4. The method ofclaim 1 in which; a. the alternating current feedback gain of saidelectrical feedback is substantially constant as a function of theattracted position of the mass.
 5. The method of claim 3, including thestep of; a. controlling the amplitude of said plural-phase alternatingcurrent as a function of its frequency, whereby the feedback gain may bemaintained substantially constant notwithstanding changes in thefrequency.
 6. The method of claim 1, including the additional step of;a. regulating the magnitude of the magnetic attraction exerted upon saidmass by control of said nonlinear feedback to provide lateral stabilityof said mass with respect to said stationary element.
 7. Magneticsuspension apparatus comprising; a. a stationary ferromagnetic member(2), b. a movable ferromagnetic member (1), disposed below saidstationary member and defining a gap between said members, c. anelectrical circuit (4, 38) associated with said movable member toproduce a magnetic flux across said gap, d. a first sensor element (22)responsive to the length of said gap, e. a second sensor element (20)responsive to motion of said movable member, and f. a nonlinear feedbackcircuit (24, 26) including said first and second sensor elements andconnected to said electrical circuit for the electrical control of saidelectrical circuit over a wide range of length of said gap.
 8. Theapparatus of claim 7 in which; a. the magnetic flux across said gap isdeveloped by alternating current applied to said electrical circuit, andb. the output of said feedback circuit is a direct current controlvoltage to control the magnitude of said alternating current.
 9. Theapparatus of claim 8 in which; a. said stationary member is an elongatedrail, and b. said movable member includes means to shift the position ofstable equilibrium along said rail.
 10. The apparatus of claim 7, inwhich; a. said stationary ferromagnetic member is a rail havingrepetitive magnetic discontinuities, and b. said electrical circuit hasplural paths (11, 12, 13) to carry plural-phase electric current toprogressively alter the position of stable magnetic equilibrium of saidmovable member wIth respect to said rail for translating said movablemember (1) along said rail.
 11. The apparatus of claim 10 in which; a.said electrical circuit is wound (11, 12, 13) for plural phases ofelectricity, and b. said magnetic discontinuities are spaced to includea part of said electrical circuit which carries all of said pluralphases.
 12. The apparatus of claim 10 in which; a. the plurality of theplural-phase paths of said electrical circuit is three.
 13. Theapparatus of claim 7 in which; a. said stationary ferromagnetic memberis a rail having discrete repetitive electrical paths, and b. saidelectrical circuit has plural paths (11, 12, 13) to carry plural-phaseelectric current, to induce electric current in said electrical pathsfor progressively altering the position of stable magnetic equilibriumof said movable member (1) with respect to said rail to translate saidmovable member along said rail.
 14. The apparatus of claim 13 whichincludes; a. electrical discontinuity conductors (115) transverse tosaid rail, and b. longitudinal shorting conductors (116, 117), theelectrical conductivity of said conductors and said shorting conductorsbeing greater than the transverse electrical conductivity of said rail.15. The apparatus of claim 7, which additionally includes; a. a uniformelectrical conductor (2'''''') substantially coextensive with andattached to the underside of said stationary ferromagnetic member (2) tolie within said gap, whereby said magnetic flux induces electriccurrents in said uniform electrical conductor to magnetically propelsaid movable ferromagnetic member (1) along said stationaryferromagnetic member.
 16. The apparatus of claim 7, which additionallyincludes; a. further plural-phase windings (111, 112, 113) repetitivelydisposed along said stationary elongated ferromagnetic member (2), b.means to energize said further plural-phase windings with plural-phaseelectric current, and c. electrically reactive means to alter the phaseof electric current flowing in said electrical circuit (4, 38) byinduction from said further plural-phase windings from the phase of theelectric current flowing in said further plural-phase windings, wherebyelectric power is transmitted from said further plural-phase windings tosaid electrical circuit.
 17. The apparatus of claim 7 in which; a. saidstationary ferromagnetic member (2) is magnetically uniform andhomogeneous, is magnetically retentive, and exhibits magnetichysteresis, whereby a longitudinal force is exerted upon said motor (1)upon electric current flowing through the electric circuit thereof. 18.The apparatus of claim 7 in which; a. said movable ferromagnetic member(1) is longitudinally laminated.
 19. The apparatus of claim 7 in whicha. said stationary ferromagnetic member (2) is longitudinally laminated.20. The apparatus of claim 7, in which said nonlinear feedback circuitincludes; a. an electrical element (24) having an electrical outputproportional to a mathematical root of the electrical input thereto. 21.The apparatus of claim 7, in which said nonlinear feedback circuitincludes; a. another electrical element (26) having an electrical outputproportional to a mathematical differential of the electrical inputthereto.
 22. The apparatus of claim 7, in which the nonlinear feedbackcircuit includes; a. an electrical integrator (58, 59, 61) connected tosaid first sensor element (22) responsive to the length of the gap, b.said integrator and also said second sensor element (20) responsive toacceleration connected to a first electrical element (24) having anelectrical output proportional to a mathematical root of the electricalinput thereto, c. the electrical output of said root element connectedto a second electrical element (26) having an electrical outputproportional to the mathematical differential of the electrical inputthereto, and d. the output of said second electrical element connectedto said electrical circuit (35, 36, 37, 38 4) associated with saidmovable ferromagnetic member (1) for the control of said electricalcircuit.
 23. The apparatus of claim 7, in which said electrical circuitincludes; a. a variable frequency plural-phase oscillator (31) tooriginate alternating electrical energy for energizing said electricalcircuit (38, 4) at a selected frequency corresponding to the desiredvelocity of translation of said movable ferromagnetic member (1). 24.The apparatus of claim 23, in which said electrical circuit additionallyincludes; a. an imperfect differentiator (32, 33 or 34) connected toeach output phase circuit if said plural-phase oscillator (31), and tosaid electrical circuit (38, 4), to give an increasing voltage outputwith increasing frequency for overcoming the inductive reactance of saidelectrical circuit (4) associated with said movable ferromagnetic member(1).
 25. The apparatus of claim 23, in which said electrical circuitadditionally includes; a. plural electrical multipliers (35, 36, 37),each having, b. a first input circuit ( phi A, phi B, phi C) connectedto an output phase circuit of said plural-phase oscillator (31), c. asecond input circuit (Y) connected to said nonlinear feedback circuit,and d. an output circuit connected to said electrical circuit (38, 4)for energizing said electrical circuit proportional to the product ofthe electrical amplitudes derived from both said oscillator and saidfeedback circuit.
 26. Magnetic suspension apparatus comprising; a.alternating current energized electromagnetic means for freelysuspending a mass by magnetic attraction against the force of gravityacting thereon, b. sensing means carried by the mass for sensingmovements thereof away from a reference position, and c. feedback meansincluding said sensing means for regulating the magnitude of thealternating current energization in accordance with movements sensed bythe sensing means to thereby restore the mass to its reference positionover a range of frequency upwards from zero.
 27. The apparatus of claim26 wherein; a. the feedback means generates a direct current feedbackvoltage for control of the magnitude of the alternating currentenergization currents.
 28. The apparatus of claim 27 wherein; a. saidfeedback voltage includes a control parameter to compensate for changesin the total weight of said mass to thereby restore the same to saidreference position notwithstanding said changes in weight.
 29. Theapparatus of claim 27 wherein; a. the feedback voltage includes acontrol parameter responsive to the velocity of movement of the mass.30. The apparatus of claim 27 wherein; a. the feedback voltage includesa control parameter responsive to the acceleration of movement of themass.
 31. The apparatus of claim 27 wherein; a. the feedback voltageincludes a control parameter responsive to the displacement of theobject from its reference position.
 32. The apparatus of claim 27wherein; a. the feedback voltage in response to said movements varies asthe product of displacement of the mass from said reference positiontimes the algebraic sum of
 33. The apparatus of claim 32 wherein; a.said displacement is a dominant factor affecting the feedback voltagewhen the frequency of changes in displacement is in the range from dc to1.2 hertz.
 34. The apparatus of claim 32 wherein; a. said accelerationis a dominant factor affecting the feedback voltage when the frequencyof changes in said displacement is in the range above 1.2 hertz.